Extreme value distribution based gene selection criteria for discriminant microarray data analysis using logistic regression

One important issue commonly encountered in the analysis of microarray data is to decide which and how many genes should be selected for further studies. For discriminant microarray data analyses based on statistical models, such as the logistic regression models, gene selection can be accomplished by a comparison of the maximum likelihood of the model given the real data, (L) over cap (D\M), and the expected maximum likelihood of the model given an ensemble of surrogate data with randomly permuted label, (L) over cap (D-0\M). Typically, the computational burden for obtaining (L) over cap (D-0\M) is immense, often exceeding the limits of available computing resources by orders of magnitude. Here, we propose an approach that circumvents such heavy computations by mapping the simulation problem to an extreme-value problem. We present the derivation of an asymptotic distribution of the extreme-value as well as its mean, median, and variance. Using this distribution, we propose two gene selection criteria, and we apply them to two microarray datasets and three classification tasks for illustration.